In many areas, we have well-founded insights about causal structure that would be useful to bring into our trained models while still allowing them to learn in a data-driven fashion. To achieve this, we present the new method of interchange intervention training(IIT). In IIT, we (1)align variables in the causal model with representations in the neural model and (2) train a neural model to match the counterfactual behavior of the causal model on a base input when aligned representations in both models are set to be the value they would be for a second source input. IIT is fully differentiable, flexibly combines with other objectives, and guarantees that the target causal model is acausal abstraction of the neural model when its loss is minimized. We evaluate IIT on a structured vision task (MNIST-PVR) and a navigational instruction task (ReaSCAN). We compare IIT against multi-task training objectives and data augmentation. In all our experiments, IIT achieves the best results and produces neural models that are more interpretable in the sense that they realize the target causal model.